Mean Robust Optimization

TL;DR

Mean robust optimization offers a flexible, data-driven approach that balances conservatism and computational efficiency by clustering data, bridging robust and distributionally robust optimization with proven guarantees.

Contribution

The paper introduces a novel clustering-based uncertainty set construction that reduces problem size and computational effort while maintaining solution quality.

Findings

Achieves significant speedups in solution time, up to multiple orders of magnitude.

Provides finite-sample guarantees and controls conservatism introduced by clustering.

Demonstrates effectiveness on numerical examples with minimal impact on solutions.

Abstract

Robust optimization is a tractable and expressive technique for decision-making under uncertainty, but it can lead to overly conservative decisions when pessimistic assumptions are made on the uncertain parameters. Wasserstein distributionally robust optimization can reduce conservatism by being data-driven, but it often leads to very large problems with prohibitive solution times. We introduce mean robust optimization, a general framework that combines the best of both worlds by providing a trade-off between computational effort and conservatism. We propose uncertainty sets constructed based on clustered data rather than on observed data points directly thereby significantly reducing problem size. By varying the number of clusters, our method bridges between robust and Wasserstein distributionally robust optimization. We show finite-sample performance guarantees and explicitly control the potential additional pessimism introduced by any clustering procedure. In addition, we prove conditions for which, when the uncertainty enters linearly in the constraints, clustering does not affect the optimal solution. We illustrate the efficiency and performance preservation of our method on several numerical examples, obtaining multiple orders of magnitude speedups in solution time with little-to-no effect on the solution quality.